   Chapter 8.2, Problem 12E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating Trigonometric Functions In Exercises 7-12, sketch a right triangle corresponding to the trigonometric function of the acute angle θ and find the values of the other five trigonometric functions of θ . csc θ = 4.25

To determine

To calculate: The values of other five trigonometric functions of θ, if cscθ=4.25.

Explanation

Given Information:

The provided trigonometric ratio cscθ=4.25.

Formula used:

Circular function definition:

sinθ=yrcscθ=rycosθ=xr         secθ=rx

And,

tanθ=yx         cotθ=xy

Where, x is the length of the side adjacent to θ, y is the length of the side opposite to θ, and r=x2+y2 is the length of hypotenuse which is not equal to 0.

Calculation:

Consider the provided trigonometric ratio, cscθ=4.25.

Since cscθ=ry, so,

From the provided trigonometric function, the value of r is 4.25 and y is 1.

So, the value of x will be;

r=x2+y24.25=x2+124.25=x2+1

Take square root both sides as;

(4.25)2=(x2+1)218.06=x2+1

Subtract 1 from both sides as;

18.061=x2+1117.06=x2

Take square root both sides as;

x2=17

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